This invention relates to a digital filtering circuit and, more particularly, to a digital filtering circuit for interpolation for use in a digital-to-analog converter (DAC) of oversampling type.
As well known in the art, the digital-to-analog converter of the oversampling type carries out a digital-to-analog (D/A) conversion operation at a higher sampling frequency which is tens of or hundreds of times as large as a normal sampling frequency or the Nyquist rate. The higher sampling frequency is called an oversampling frequency. By using the oversampling frequency, it is possible to distribute quantizing noise into a wider frequency area and resulting in decreasing the quantizing noise in a desired frequency band. This means that it is possible to improve a signal-to-noise ratio (S/N) by sampling at the oversampling frequency although quantization bit number is the same on D/A conversion. It is therefore possible to reduce the quantization bit number by using the oversampling frequency with respect to the same signal-to-noise ratio.
In addition, in D/A conversion, an image signal necessarily generates in out-of-band. To remove the image signal, an analog filter is necessary. Such an analog filter is referred to as a post-filter. A normal digital-to-analog converter of no oversampling type is called a digital-to-analog converter of the Nyquist sampling type. It is necessary for the digital-to-analog converter of the Nyquist sampling type to use a high accuracy post-filter which has a rapid frequency characteristic to remove the image signal. By using the digital-to-analog converter of the oversampling type, the post-filter is implemented by a filter which is simple in structure and it is possible to reduce analog circuits. However, the image signal is present at every Nyquist sampling frequency if data of the Nyquist sampling frequency is directly converted to an analog signal at the oversampling frequency. As a result, it is impossible to reduce a characteristic of the post-filter. In the digital-to-analog converter of the oversampling type, in order to reduce the characteristic of the post-filter, the image signal is removed by a digital filter. The digital filter is called an interpolation filter.
The interpolation filter comprises first through M-th digital filtering circuits, where M represents a positive integer which is not less than two. The first stage digital filtering circuit has a function of a low-pass filter for removing the image signal having a high frequency. To reduce a scale of a digital circuit, the first stage digital filtering circuit is operable as a first sampling frequency which is higher than the Nyquist sampling frequency and is lower than the oversampling frequency. The second through the M-th stage digital filtering circuits are operable as second through M-th sampling frequencies, respectively, which rise in ascending order. The M-th sampling frequency is equal to the oversampling frequency. Inasmuch as an image signal may occupy all over the frequency range except for the desired frequency band dependent on an input signal thereof, the first stage digital filtering circuit must attenuate the image signal in the above-mentioned frequency range. Each of the second through the M-th stage digital filtering circuits may use a filter having a comb-shaped characteristic because an image signal in low-pass filter output occupies only every Nyquist sampling frequency in all of the frequency range of the out-of-band.
The first stage digital filtering circuit must use an advanced low-pass filter implemented by a digital signal processor (DSP). This is because it is necessary to attenuate all of signals laid on the out-of-band as mentioned before. However, each of the second through the M-th stage digital filtering circuits may use a filter which is simple in structure and which is called a moving average filter. This is because this filter may be realized by the filter having the comb-shaped characteristic as mentioned before. Inasmuch as only one moving average filter has an insufficient attenuation to attenuate the image signal, a plurality of moving average filters are used to obtain a sufficient attenuation for the image signal.
In general, the moving average filter is implemented by a finite impulse response (FIR) type filter. Inasmuch as a plurality of FIR type filters must be used, it results in increasing a scale of the circuit. To resolve this defect, a linear interpolating circuit is disclosed in an article which is contributed by James C. Candy et al to IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-29, No. 6 (June 1981), pages 815-830, and which has a title of "A Voiceband Codec with Digital Filtering." The linear interpolating circuit serves as a two-stage moving average filter. The linear interpolating circuit raises a sampling frequency of an input data signal thereof to an oversampling frequency which is N times the sampling frequency by linearly interpolating (N-1) interpolation data elements between each pair of consecutive input data elements (a current input data element IDc and a previous input data element IDp) appearing at the low-pass filter output, where N represents a predetermined positive integer which is not less than two. The (N-1) interpolation data elements linearly change between the current input data element IDc and the previous input data element IDp as mentioned before. As a result, the linear interpolating circuit produces an output data signal consisting of a plurality of output data elements each of which has variation V which is represented by: EQU V=(IDc-IDp)/N.
In addition, the previous input data element IDp is always obtained by the output data elements.
In the manner which will later be described, a conventional digital filtering circuit is advantageous in that it occupies a large area on a large scale integration (LSI) chip. In addition, it is necessary to manually reset the digital filtering circuit on malfunction.